Maximum Likelihood Estimation in Gaussian Chain Graph Models under the Alternative Markov Property

The AMP Markov property is a recently proposed alternative Markov property for chain graphs. In the case of continuous variables with a joint multivariate Gaussian distribution, it is the AMP rather than the earlier introduced LWF Markov property that is coherent with data-generation by natural block-recursive regressions. In this paper, we show that maximum likelihood estimates in Gaussian AMP chain graph models can be obtained by combining generalized least squares and iterative proportional fitting to an iterative algorithm. In an appendix, we give useful convergence results for iterative partial maximization algorithms that apply in particular to the described algorithm.Comment: 15 pages, article will appear in Scandinavian Journal of Statistic

The physical determinants of the thickness of lamellar polymer crystals

Based upon kinetic Monte Carlo simulations of crystallization in a simple polymer model we present a new picture of the mechanism by which the thickness of lamellar polymer crystals is constrained to a value close to the minimum thermodynamically stable thickness. This description contrasts with those given by the two dominant theoretical approaches.Comment: 4 pages, 4 figures, revte

Divergence functions in Information Geometry

A recently introduced canonical divergence $\mathcal{D}$ for a dual structure $(\mathrm{g},\nabla,\nabla^*)$ is discussed in connection to other divergence functions. Finally, open problems concerning symmetry properties are outlined.Comment: 10 page

Bayesian optimization of the PC algorithm for learning Gaussian Bayesian networks

The PC algorithm is a popular method for learning the structure of Gaussian Bayesian networks. It carries out statistical tests to determine absent edges in the network. It is hence governed by two parameters: (i) The type of test, and (ii) its significance level. These parameters are usually set to values recommended by an expert. Nevertheless, such an approach can suffer from human bias, leading to suboptimal reconstruction results. In this paper we consider a more principled approach for choosing these parameters in an automatic way. For this we optimize a reconstruction score evaluated on a set of different Gaussian Bayesian networks. This objective is expensive to evaluate and lacks a closed-form expression, which means that Bayesian optimization (BO) is a natural choice. BO methods use a model to guide the search and are hence able to exploit smoothness properties of the objective surface. We show that the parameters found by a BO method outperform those found by a random search strategy and the expert recommendation. Importantly, we have found that an often overlooked statistical test provides the best over-all reconstruction results

A Bayesian Approach to Inverse Quantum Statistics

A nonparametric Bayesian approach is developed to determine quantum potentials from empirical data for quantum systems at finite temperature. The approach combines the likelihood model of quantum mechanics with a priori information over potentials implemented in form of stochastic processes. Its specific advantages are the possibilities to deal with heterogeneous data and to express a priori information explicitly, i.e., directly in terms of the potential of interest. A numerical solution in maximum a posteriori approximation was feasible for one--dimensional problems. Using correct a priori information turned out to be essential.Comment: 4 pages, 6 figures, revte

A Neural Circuit Arbitrates between Persistence and Withdrawal in Hungry Drosophila

In pursuit of food, hungry animals mobilize significant energy resources and overcome exhaustion and fear. How need and motivation control the decision to continue or change behavior is not understood. Using a single fly treadmill, we show that hungry flies persistently track a food odor and increase their effort over repeated trials in the absence of reward suggesting that need dominates negative experience. We further show that odor tracking is regulated by two mushroom body output neurons (MBONs) connecting the MB to the lateral horn. These MBONs, together with dopaminergic neurons and Dop1R2 signaling, control behavioral persistence. Conversely, an octopaminergic neuron, VPM4, which directly innervates one of the MBONs, acts as a brake on odor tracking by connecting feeding and olfaction. Together, our data suggest a function for the MB in internal state-dependent expression of behavior that can be suppressed by external inputs conveying a competing behavioral drive

Kinetic Model for Layer-by-Layer Crystal Growth in Chain Molecules

A kinetic model is proposed to describe the structure and rate of advancement of the growth front during crystallization. Solidification occurs through the mechanisms of surface nucleation and lateral spreading of the solid phase within layers in the vicinity of the growth front. The transformation from liquid to solid within each layer is described by an equation similar to the two-dimensional variant of the Johnson–Mehl–Avrami (JMA) equation, but in which the finite size and shape of the critical nucleus and the dynamic evolution of the solid fraction of the underlying layers are taken into account. Connection to the regime theory of Hoffman and co-workers, for surface nucleation and spreading in one or two dimensions, is also made. Given only molecular level information regarding surface nucleation rates, lateral spreading rates, and critical surface nucleus geometry, the resulting set of coupled nonlinear equations for solidification in each layer is numerically integrated in time to obtain the structure and rate of advancement of the growth front, for arbitrarily large systems and long times. Using this kinetic model with input parameters obtained from molecular dynamics simulations, a multiscale modeling analysis of crystal growth in n-pentacontane (C50) is performed.National Science Foundation (U.S.) Division of Civil, Mechanical and Manufacturing Innovation (CMMI-1235109

Solid State Systems for Electron Electric Dipole Moment and other Fundamental Measurements

In 1968, F.L. Shapiro published the suggestion that one could search for an electron EDM by applying a strong electric field to a substance that has an unpaired electron spin; at low temperature, the EDM interaction would lead to a net sample magnetization that can be detected with a SQUID magnetometer. One experimental EDM search based on this technique was published, and for a number of reasons including high sample conductivity, high operating temperature, and limited SQUID technology, the result was not particularly sensitive compared to other experiments in the late 1970's. Advances in SQUID and conventional magnetometery had led us to reconsider this type of experiment, which can be extended to searches and tests other than EDMs (e.g., test of Lorentz invariance). In addition, the complementary measurement of an EDM-induced sample electric polarization due to application of a magnetic field to a paramagnetic sample might be effective using modern ultrasensitive charge measurement techniques. A possible paramagnetic material is Gd-substituted YIG which has very low conductivity and a net enhancement (atomic enhancement times crystal screening) of order unity. Use of a reasonable volume (100's of cc) sample of this material at 50 mK and 10 kV/cm might yield an electron EDM sensitivity of $10^{-33}$ e cm or better, a factor of $10^6$ improvement over current experimental limits.Comment: 6 pages. Prepared for ITAMP workshop on fundamental physics that was to be held Sept 20-22 2001 in Cambride, MA, but was canceled due to terrorist attack on U.S New version incorporates a number of small changes, most notably the scaling of the sensitivity of the Faraday magnetometer with linewidth is now treated in a saner fashion. The possibility of operating at an even lower temperarture, say 10 microkelvin, is also discusse

Estimation of Parameters in DNA Mixture Analysis

In Cowell et al. (2007), a Bayesian network for analysis of mixed traces of DNA was presented using gamma distributions for modelling peak sizes in the electropherogram. It was demonstrated that the analysis was sensitive to the choice of a variance factor and hence this should be adapted to any new trace analysed. In the present paper we discuss how the variance parameter can be estimated by maximum likelihood to achieve this. The unknown proportions of DNA from each contributor can similarly be estimated by maximum likelihood jointly with the variance parameter. Furthermore we discuss how to incorporate prior knowledge about the parameters in a Bayesian analysis. The proposed estimation methods are illustrated through a few examples of applications for calculating evidential value in casework and for mixture deconvolution